<< 1 >>
Rating: 
Summary: The best text I had as a graduate student
Review: One of the first classes I took as a graduate student in mathematics was in the foundations of mathematics. The topic was set theory and this was the text we used. There have been many times in my mathematical career that I have been grateful for the knowledge learned in the class and this is one of two course textbooks that I still regularly consult as a reference. It is an excellent introduction to the fundamentals of set theory and ordinal arithmetic and I heartily recommend this book to anyone teaching or learning the fundamentals of sets.
Rating:
Summary: Close to Perfect
Review: This is pretty much the perfect introduction to set theory for someone having some familiarity with rigorous mathematics. The treatment is axiomatic but doesn't employ the usual logical formalism, everything is written in plain english. The book emphasizes the foundational character of set theory and shows how all the usual objects of mathematics can be developed using only sets. It also demonstrates the application of set theoretic methods to "ordinary" mathematics by giving complete proofs of some powerful theorems like the Hahn-Banach theorem in functional analysis. The pace is leisurely with a close look at the details. The axiom of choice is used only when necessary and it's uses are highlighted. The exercises contain real meat but are broken up in handable pieces. They also give alternative approaches to topics treated in the main text. Solutions are not contained. The last section is devoted to an outlook at more advanced set theory. The ideas of the constructible universe and of forcing are outlined, as far as that is possible on that level. There is also a discussion on candidates for additional axioms. The reader will gain both insight into what set theory is and how powerful it is. There is no better book for the same audience.
<< 1 >>
| 
